Representation theory I - finite groups

MATH-314 / 5 credits

Teacher: Lachowska Anna

Language: English

Summary

This is a standard course in representation theory of finite groups.

Content

This course is an introduction to representation theory. We study the basic notions and results in representations of finite groups. The classical character theory is treated in detail with many examples. In particular, we study the representations of symmetric groups over complex numbers.

Keywords

Representation, subrepresentation, irreducible representation, character, character tables, tensor product of representations, induced representation.

Learning Prerequisites

Required courses

Linear algebra

Recommended courses

Abstract algebra: groups

Learning Outcomes

By the end of the course, the student must be able to:

  • Analyze representations of a finite group
  • Identify irreducible representation, subrepresentation
  • Compute character of a representation
  • Construct an induced representation
  • Analyze a tensor product of representations

Teaching methods

Lectures and problem sessions.

Assessment methods

One written homework (15% of the grade) and a written exam (85% of the grade).

Supervision

Assistants Yes
Forum Yes

Resources

Bibliography

P. Etingof et al., "Introduction to Representation Theory"

W. Fulton, J.Harris, "Representation Theory: A first course"

Ressources en bibliothèque

Moodle Link

In the programs

  • Semester: Fall
  • Exam form: Written (winter session)
  • Subject examined: Representation theory I - finite groups
  • Courses: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Type: optional

Reference week

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